Abstract
This paper presents normal form expressions of Propositional Projection Temporal Logic (PPTL). For doing so, a PPTL formula is represented as the disjunction of formulas in form of \(e_\varepsilon^k=\bigwedge_{0\leq i\leq k\in N_0} \bigcirc^iS_i\wedge \bigcirc^k\varepsilon\) or \(e_\omega^{(k,l)}=\bigwedge_{0\leq i\leq k\in N_0} \bigcirc^iS_i\wedge\bigwedge_{k\leq j\in N_\omega}\bigcirc^j(\bigcirc S_{k+1}\wedge\bigcirc^2 S_{k+2}\wedge \cdots\wedge\bigcirc^l S_{k+l}),1\leq l\in N_0\). Here \(e_\varepsilon^k\) denotes a finite model with length being k while \(e_\omega^{(k,l)}\) indicates an infinite model. We show that any PPTL formula can be expressed as a normal form expression. As a consequence, satisfiability of PPTL formulas can easily be achieved.
The research is supported by the National Program on Key Basic Research Project of China (973 Program) Grant No.2010CB328102, National Natural Science Foundation of China under Grant No. 61133001, 61202038, 61272117, 61272118, 61322202 and 91218301.
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Duan, Z., Tian, C., Zhang, N. (2014). Normal Form Expressions of Propositional Projection Temporal Logic. In: Cai, Z., Zelikovsky, A., Bourgeois, A. (eds) Computing and Combinatorics. COCOON 2014. Lecture Notes in Computer Science, vol 8591. Springer, Cham. https://doi.org/10.1007/978-3-319-08783-2_8
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DOI: https://doi.org/10.1007/978-3-319-08783-2_8
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